Optimizing the Geometric Programming Problem with Single-Term Exponents Subject to Max-Product Fuzzy Relational Equation

In this paper, we investigate the problem of minimizing objective function with single-term exponents subject to fuzzy relational equation specified in max-product composition. Two folds are presented. Firstly, we present some properties for this optimization problem under the assumption of both negative and nonnegative exponents in the objective function. Second, the new efficient method called min-max methods is provided to find an optimal solution without looking for all the potential minimal solutions. Numerical example is given to illustrate the feasibility of the present method.

[1]  Jiranut Loetamonphong,et al.  Optimization of fuzzy relation equations with max-product composition , 2001, Fuzzy Sets Syst..

[2]  W. Pedrycz,et al.  Fuzzy relation equations on a finite set , 1982 .

[3]  W. Pedrycz,et al.  Fuzzy Relation Equations and Their Applications to Knowledge Engineering , 1989, Theory and Decision Library.

[4]  Paul P. Wang,et al.  Fuzzy relation equations (I): the general and specialized solving algorithms , 2002, Soft Comput..

[5]  Shu-Cherng Fang,et al.  Solving fuzzy relation equations with a linear objective function , 1999, Fuzzy Sets Syst..

[6]  Jihui Yang,et al.  Monomial geometric programming with fuzzy relation equation constraints , 2007, Fuzzy Optim. Decis. Mak..

[7]  W. Pedrycz.  ON GENERALIZED FUZZY RELATIONAL EQUATIONS AND THEIR APPLICATIONS , 1985 .

[8]  Yang Ji-hui,et al.  Geometric Programming with Fuzzy Relation Equation Constraints , 2006 .

[9]  Pei-Zhuang Wang,et al.  Latticized linear programming and fuzzy relation inequalities , 1991 .

[10]  Elie Sanchez,et al.  Resolution of Composite Fuzzy Relation Equations , 1976, Inf. Control..

[11]  A. V. Markovskii,et al.  On the relation between equations with max-product composition and the covering problem , 2005, Fuzzy Sets Syst..

[12]  Shu-Cherng Fang,et al.  Solving nonlinear optimization problems with fuzzy relation equation constraints , 2001, Fuzzy Sets Syst..

[13]  Yan-Kuen Wu,et al.  Minimizing a linear function under a fuzzy max-min relational equation constraint , 2005, Fuzzy Sets Syst..

[14]  Yan-Kuen Wu.  Optimizing the geometric programming problem with single-term exponents subject to max-min fuzzy relational equation constraints , 2008, Math. Comput. Model..